Smyth was born in Drogheda, County Louth. He turned professional in 1974 and was a member of the European Tour for over a quarter of a century. His best finish on the European Tour Order of Merit was seventh in 1988. He won eight tournaments on the tour across four different decades, breaking Neil Coles' record as the oldest man to win a European Tour event when he claimed the 2001 Madeira Island Open at the age of 48 years and 34 days. This record was broken by Miguel Ángel Jiménez (48 years, 11 months, 13 days) at the 2012 UBS Hong Kong Open.